Suppose that for a random sample of 250 firms that revalued their fixed assets, the mean ratio of debt to tangibleassets was 0.624, and the sample standard deviation was 0.172. For an independent random sample of 450 firmsthat did not revalue their fixed assets, the mean ratio of debt to tangible assets was 0.594, and the sample standarddeviation was 0.164. Assuming that the population distributions are normal with equal variances, find a 99%confidence interval for the difference between the two population means.Click the icon to view a table of upper critical values of Student's t distribution.A 99% confidence interval for the difference between the two population means is (.). (Round to four decimalplaces as needed.)

Answered: Image /qna-images/answer/ad01de3b-3a26-49cf-8bdd-76d92f45ff43.jpg

Answered: Suppose that for a random sample of 250…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Suppose that an accounting firm does a study to determine the time needed to complete one person's tax forms. It randomly surveys 175 people. The sample mean is 23.1 hours. There is a known population standard deviation of 6.6 hours. The population distribution is assumed to be normal.NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)
Suppose a mutual fund qualifies as having moderate risk if the standard deviation of its monthly rate of return is less than 4%. A mutual-fund rating agency randomly selects 26 months and determines the rate of return for a certain fund. The standard deviation of the rate of return is computed to be 3.48%. Is there sufficient evidence to conclude that the fund has moderate risk at the alpha equals 0.05 level of significance? A normal probability plot indicates that the monthly rates of return are normally distributed. a. Calculate the value of the test statistic. chi squared equals (Round to three decimal places as needed.) b. Use technology to determine the P-value for the test statistic. The P-value is (Round to three decimal places as needed.)
Suppose that an accounting firm does a study to determine the time needed to complete one person's tax forms. It randomly surveys 175 people. The sample average is 23.1 hours. There is a known population standard deviation of 7.0 hours. The population distribution is assumed to be normal. NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) O Part (a) (i) (ii) (ii) (rounded to three decimal places) (iv) n = (v) n- 1= O Part (b) O Part (c) O Part (d) Construct a 90% confidence interval for the population average time to complete the tax forms. (i) State the confidence interval. (Round your answers to two decimal places.) (ii) Sketch the graph. a C.L. = (iii) Calculate the error bound. (Round your answer to two decimal places.)
A sample of 15 small bags of the same brand of candies was selected. Assume that the population distribution of bag weights is normal. The weight of each bag was then recorded. The mean weight was 2 ounces with a standard deviation of 0.12 ounces. The population standard deviation is known to be 0.1 ounce. NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) O Part (a) (i) x= (ii) (iii) sy = (iv) n = (v) n- 1 = O Part (b) O Part (c) O Part (d) Which distribution should you use for this problem? (Round your answers to three decimal places.) Explain your choice. O The Student's t-distribution should be used because the sample size is small. O The standard normal distribution should be used because the sample standard deviation is known. O The Student's t-distribution should be used because the sample standard deviation is given. O The standard normal…
Assume the average amount of caffeine consumed daily by adults is normally distributed with a mean of 260 mg and a standard deviation of 48 mg. In a random sample of 600 adults, how many consume at least 320 mg of caffeine daily?
Suppose a mutual fund qualifies as having moderate risk if the standard deviation of its monthly rate of return is less than 6%. A mutual-fund rating agency randomly selects 25 months and determines the rate of return for a certain fund. The standard deviation of the rate of return is computed to be 4.21%. Is there sufficient evidence to conclude that the fund has moderate risk at the alpha equals 0.05 level of significance? A normal probability plot indicates that the monthly rates of return are normally distributed. a. Calculate the value of the test statistic. chi squared equals (Round to three decimal places as needed.) b. Use technology to determine the P-value for the test statistic. The P-value is (Round to three decimal places as needed.)
1. The strength of steel wire made by an existing process is normally distributed with a mean of 1550 and a standard deviation of 170. A batch of wire is made by a new process, and a random sample consisting of 25 measurements gives an average strength of 1316. Assume that the standard deviation does not change. Is there evidence at the 1% level of significance that the new process gives a larger mean strength than the old? To answer this question, the null hypothesis could be stated as A. μ= 1550 psi B. μ> 1550 psi C.µ + 1550 psi D. μ< 1550 psi
Suppose that an accounting firm does a study to determine the time needed to complete one person's tax forms. It randomly surveys 175 people. The sample mean is 22.4hours. There is a known population standard deviation of 6.2 hours. The population distribution is assumed to be normal. NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) Which distribution should you use for this problem? Construct a 90% confidence interval for the population mean time to complete the tax forms
A sample of 17 small bags of the same brand of candies was selected. Assume that the population distribution of bag weights is normal. The weight of each bag was then recorded. The mean weight was 2 ounces with a standard deviation of 0.13 ounces. The population standard deviation is known to be 0.1 ounce.NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) Find the following. (Round your answers to two decimal places.) (i) x = (ii) ? = (iii) sx = Which distribution should you use for this problem? (Round your answers to three decimal places.) X ~ ,
E
5. The standard deviation of a sample of the costs of 15 automobile repairs at a local garage was $120.82. Assuming that the variable is normally distributed, find the critical values, Xleft and right, that could be used to determine the 90% confidence interval of the true variance and standard deviation.
Recent studies have shown that about 39.9% of American adults fit the medical definition of being obese. A large medical clinic would like to estimate what percentage of their patients are obese, so they take a random sample of 400 patients and find that 136 are obese. Suppose that in truth, the same percentage holds for the patients of the medical clinic as for the general population, 39.9%. The standard deviation of the sampling distribution of was found to be 0.0245. If the clinic took repeated random samples of 400 observations and found the sample proportion who were obese, into what interval should those sample proportions fall about 95% of the time? (Use the Empirical Rule. Round your answers to two decimal places.) between and

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